Problem: What's the first wrong statement in the proof below that $ \triangle ABC \cong \triangle EBC$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \overline{BD} \cong \overline{BC}$ $, \ $ $ \angle DBE \cong \angle ABC$ $, \ $ $ \angle BED \cong \angle BAC$ $, \ $ $ \overline{CF} \cong \overline{BC}$ $, \ $ $ \angle CFE \cong \angle ABC$ $, \ $ and $\ $ $ \overline{EF} \cong \overline{AB}$ Proof $ \triangle ABC \cong \triangle EBD$ because AAS $ \overline{AB} \cong \overline{BE}$ because corresponding parts of congruent triangles are congruent $ \triangle EBC \cong \triangle ABC$ because AAS $ \triangle EFC \cong \triangle ABC$ because SAS $ \overline{CE} \cong \overline{AC}$ because corresponding parts of congruent triangles are congruent
Solution: Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. $ \triangle ABC \cong \triangle EBC$ is the first wrong statement.